On the extension of the concept of Thin Shells to The Einstein-Cartan Theory

TL;DR

This paper extends the formalism of thin shells to Einstein-Cartan theory, incorporating torsion and curvature constraints, and derives surface stress-energy tensors and solutions including null shells of matter.

Contribution

It introduces a formalism for thin shells in Einstein-Cartan theory, accounting for torsion and curvature constraints, and constructs explicit solutions with null hypersurfaces.

Findings

Derived general expression for surface stress-energy tensor in Einstein-Cartan theory.

Established conditions under which thin shells can be described within this framework.

Constructed a null shell of matter as an application of the formalism.

Abstract

This paper develops a theory of thin shells within the context of the Einstein-Cartan theory by extending the known formalism of general relativity. In order to perform such an extension, we require the general non symmetric stress-energy tensor to be conserved leading, as Cartan pointed out himself, to a strong constraint relating curvature and torsion of spacetime. When we restrict ourselves to the class of space-times satisfying this constraint, we are able to properly describe thin shells and derive the general expression of surface stress-energy tensor both in its four-dimensional and in its three-dimensional intrinsic form. We finally derive a general family of static solutions of the Einstein-Cartan theory exhibiting a natural family of null hypersurfaces and use it to apply our formalism to the construction of a null shell of matter.